This invention relates to interferometers, e.g., linear and angular displacement measuring and dispersion interferometers, that measure linear and angular displacements of a measurement object such as a mask stage or a wafer stage in a lithography scanner or stepper system, and also interferometers that monitor wavelength and determine intrinsic properties of gases.
Displacement measuring interferometers monitor changes in the position of a measurement object relative to a reference object based on an optical interference signal. The interferometer generates the optical interference signal by overlapping and interfering a measurement beam reflected from the measurement object with a reference beam reflected from the reference object.
In many applications, the measurement and reference beams have orthogonal polarizations and different frequencies. The different frequencies can be produced, for example, by laser Zeeman splitting, by acousto-optical modulation, or internal to the laser using birefringent elements or the like. The orthogonal polarizations allow a polarizing beam-splitter to direct the measurement and reference beams to the measurement and reference objects, respectively, and combine the reflected measurement and reference beams to form overlapping exit measurement and reference beams. The overlapping exit beams form an output beam that subsequently passes through a polarizer. The polarizer mixes polarizations of the exit measurement and reference beams to form a mixed beam. Components of the exit measurement and reference beams in the mixed beam interfere with one another so that the intensity of the mixed beam varies with the relative phase of the exit measurement and reference beams.
A detector measures the time-dependent intensity of the mixed beam and generates an electrical interference signal proportional to that intensity. Because the measurement and reference beams have different frequencies, the electrical interference signal includes a “heterodyne” signal having a beat frequency equal to the difference between the frequencies of the exit measurement and reference beams. If the lengths of the measurement and reference paths are changing relative to one another, e.g., by translating a stage that includes the measurement object, the measured beat frequency includes a Doppler shift equal to 2νnp/λ, where ν is the relative speed of the measurement and reference objects, λ is the wavelength of the measurement and reference beams, n is the refractive index of the medium through which the light beams travel, e.g., air or vacuum, and p is the number of passes to the reference and measurement objects. Changes in the phase of the measured interference signal correspond to changes in the relative position of the measurement object, e.g., a change in phase of 2π corresponds substantially to a distance change L of λ/(2np). Distance 2L is a round-trip distance change or the change in distance to and from a stage that includes the measurement object. In other words, the phase Φ, ideally, is directly proportional to L, and can be expressed as                                                                         Φ                =                                  2                  ⁢                                                                           ⁢                  p                  ⁢                                                                           ⁢                  k                  ⁢                                                                           ⁢                  L                                            ,                                                                                          where                ⁢                                                                   ⁢                k                            =                                                                    2                    ⁢                                                                                   ⁢                    π                    ⁢                                                                                   ⁢                    n                                    λ                                .                                                                        (        1        )            
Unfortunately, the observable interference phase, {tilde over (Φ)}, is not always identically equal to phase Φ. Many interferometers include, for example, non-linearities such as those known as “cyclic errors.” The cyclic errors can be expressed as contributions to the observable phase and/or the intensity of the measured interference signal and have a sinusoidal dependence on the change in for example optical path length 2pnL. In particular, a first order cyclic error in phase has for the example a sinusoidal dependence on (4πpnL)/λ and a second order cyclic error in phase has for the example a sinusoidal dependence on 2(4πpnL)/λ. Higher order cyclic errors can also be present as well as sub-harmonic cyclic errors and cyclic errors that have a sinusoidal dependence of other phase parameters of an interferometer system comprising detectors and signal processing electronics. Different techniques for quantifying such cyclic errors are described in commonly owned U.S. Pat. Nos. 6,137,574, 6,252,688, and 6,246,481 by Henry A. Hill.
There are in addition to the cyclic errors, non-cyclic non-linearities or non-cyclic errors. One example of a source of a non-cyclic error is the diffraction of optical beams in the measurement paths of an interferometer. Non-cyclic error due to diffraction has been determined for example by analysis of the behavior of a system such as found in the work of J.-P. Monchalin, M. J. Kelly, J. E. Thomas, N. A. Kurnit, A. Szöke, F. Zemike, P. H. Lee, and A. Javan, “Accurate Laser Wavelength Measurement With A Precision Two-Beam Scanning Michelson Interferometer,” Applied Optics, 20(5), 736-757, 1981.
A second source of non-cyclic errors is the effect of “beam shearing” of optical beams across interferometer elements and the lateral shearing of reference and measurement beams one with respect to the other. Beam shears can be caused, for example, by a change in direction of propagation of the input beam to an interferometer or a change in orientation of the object mirror in a double pass plane mirror interferometer such as a differential plane mirror interferometer (DPMI) or a high stability plane mirror interferometer (HSPMI).
Accordingly, due to errors such as the aforementioned cyclic and non-cyclic errors, the observable interference phase typically includes contributions in addition to Φ. Thus, the observable phase is more accurately expressed as{tilde over (Φ)}=Φ+ψ+ζ,  (2)where ψ and ζ are the contributions due to the cyclic and non-cyclic errors, respectively.
In displacement measuring applications, the observable phase is often assumed equal to 2pkL, which allows one to readily determine L from the measured phase. In many cases, this is a reasonable approximation, particularly where the contribution to due cyclic and/or non-cyclic errors are small, or the level of accuracy required by the application is relatively low. However, in applications demanding a high level of precision, cyclic and/or non-cyclic errors should be accounted for. For example, high precision displacement measurement requirements of integrated circuit micro-lithography fabrication have become very demanding, in part because of the small field limitations of imaging systems in steppers and scanners and in part because of the continuing reduction in the size of trace widths on wafers. The requirement of high precision displacement measurement with steppers and scanners is typically served with plane mirror interferometers with one of the external mirrors of the plane mirror interferometers attached to a stage mirror of the stepper or scanner. Because the wafer is typically not flat, the orientation of the wafer stage of a stepper or scanner must also be adjusted in one or more angular degrees of freedom to compensate for the non-flatness of the wafer at exposure sites on a wafer. The combination of the use of plane mirror interferometers and the change in one or more angular degrees of freedom is a source of lateral shear of optical beams across interferometer elements. Effects of beam shears of a reference beam and a measurement beam may be represented effectively as a common mode beam shear and a differential beam shear. The differential beam shear is the difference in lateral shear of reference and measurement and the common mode beam shear is the average lateral shear of the reference and measurement beams.
The cited source of lateral beam shear presents a potentially serious problem in distance measuring interferometry. For a measurement leg length of 1 meter, a typical value for a change in angular orientation of a stage mirror of 0.0005 radians, and a double-pass plane mirror interferometer, the relative lateral shear between the reference and the measurement components of the output beam of the interferometer is 2 millimeters. For a relative lateral shear of 2 millimeters, a beam diameter of 6 millimeters, and wavefront errors in the output beams of the order of λ/20, an error will be generated in the inferred distance measurement of >/˜1 nanometer. This error is a non-cyclic error and can pose a serious limitation to micro-lithographic applications of steppers and scanners in integrated circuit fabrication.
Wavefront errors are produced by imperfections in transmissive surfaces and imperfections in components, e.g., retroreflectors and phase retardation plates, and/or coupling into single-mode and multi-mode optical fibers that produce undesired deformations of wavefronts of beams. Non-cyclic errors are also introduced in coupling into different longitudinal modes of a multi-mode optical fiber as a result of beam shears at the coupling interface to the multi-mode optical fiber.
In dispersion measuring applications, optical path length measurements are made at multiple wavelengths, e.g., 532 nanometers and 1064 nanometers, and are used to measure dispersion of a gas in the measurement path of a distance measuring interferometer. The dispersion measurement can be used to convert a change in optical path length measured by the distance measuring interferometer into a corresponding change in physical length. Such a conversion can be important since changes in the measured optical path length can be caused by gas turbulence and/or by a change in the average density of the gas in the measurement arm even though the physical distance to the measurement object is unchanged.
When working to position-measurement accuracy of approximately one nanometer or better and for distance measuring interferometry using dispersion interferometry to correct for the effects of gas in the measuring path, the cited non-cyclic errors are amplified by the reciprocal dispersive power of the gas, Γ. For the Nb:YAG laser beam with a wavelength of 1064 nm and the frequency doubled Nb:YAG laser with a beam wavelength of 532 nanometers, Γ≡75. For the 633 nanometer HeNe laser beam and a second beam at 316 nanometer, Γ≡25. Thus, for high-accuracy interferometry (accuracy in the 1 nanometer regime or better) it is necessary to reduce the effect of the lateral beam shear induced non-cyclic errors in the dispersion interferometry by approximately two orders of magnitude beyond that required for the corresponding distance measuring interferometry, an accuracy in the 0.01 nanometer regime or better.
Both common mode and differential beam shear can further compromise the accuracy of an interferometer where the interferometer output beam is coupled into a fiber optic pick-up (FOP) to transport the interferometer output beam to a remotely located detector.